Geodesic
On simple ideal hyperbolic Coxeter polytopes
Izvestiya. Mathematics , Tome 72 (2008) no. 1, pp. 113-126

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We prove that no simple ideal Coxeter polytope exists in the hyperbolic space $\mathbb H^n$ of dimension $n>8$.
Keywords: Coxeter polytope, hyperbolic geometry, ideal polytope, simple polytope. 
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     title = {On simple ideal hyperbolic {Coxeter} polytopes},
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P. V. Tumarkin; A. A. Felikson. On simple ideal hyperbolic Coxeter polytopes. Izvestiya. Mathematics , Tome 72 (2008) no. 1, pp. 113-126. http://geodesic.mathdoc.fr/item/IM2_2008_72_1_a5/